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Problem 18 Medium Difficulty

(a) Find the current in each resistor of Figure P 18.18 by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoff’s laws: one with the node rule; a second using the loop rule through the battery, the $6.0-\Omega$ resistor, and the $24.0-\Omega$ resistor; and the third using the loop rule through the $12.0-\Omega$ and $24.0-\Omega$ resistors. Solve to check the answers found in part (a).

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Video Transcript

in stepped A. We need to find the current which are flowing through Individual resistance is so Let's start with that tip, eh? Now here I 12 24 and I six. These other individuals currents which are flowing through the respective distances are put bless and miners across their distances got under bridges and getting endured a distance. The polarity will be plus and leaving the resistance. The polarity will be minus. You know, we tried to find the effect. You're a distance off the battler combination off 12. 24. So let's take this pattern combination as our baby. It will be 12 into 24 born trove. Blessed rifle. Here we get Answer as it comes now. Therefore, the total resistance will be this age room in cities with six homes. So that is 14 arms. So therefore coat over a distance off. The given combination is off 40 gnomes we can find. I don't know. That is total current flowing through the combination which will be digging a C. I. The amount of back reward age has given us 42 wars upon our Toto using simply oh miso. So that is coming as 42 world upon 14 homes. So we're just three amperes so that Karen was just going to The circuit is off three amperes Now this is the same current which is actually offering through six Home. Therefore I six. Home is equal to three Arab years. This is the fourth time this year No, let's find the word did across 60 to recognize the Borg age it grows. Six Home is given a serious exhumed. Therefore using homes low res equal toe I multiplied by our So we six So music or two currently just flowing through six home multiplied by 600 district So we just three amperes Mikey applied basic So dead For where? Gage across six soon he's off 18 words Now really make use of this. Ask for the warden gave distribution in series circuit We can write one equation and that equation is re six home Bless be Abie is equal to 42 weeks now The market is particular Lord as a and B So where did you grow C and B But I will find out therefore re six home is again works Yes, We Abie music will do 40 tools Therefore who did you cross? A B was coming Gas 20 forms. So by using this value we can get got into Gretel is equal to really be appoint wellems So 20 forward You ready to buy to alone Therefore current which is going through treadle He's off to abuse This is a signature that we of court No, that's fine. The cutting through 24 on the right distance again saying it will be a baby upon the value for distance You were just making use off alms low here So 24 work So do I. Did buy 24 homes which is it? Quit Do one Ambu Therefore, let me write it as I 24 Oh, home is equal to one ampere So these are the 31 years off currents that we have got to know So write the statement as so the current curtains in each but this show off six or hello and 24 home are three amperes to amperes and one and beer respectively. Let's start with step be in which we need to write the question for three current surging get jobs laws. The first we would no Drew. Yeah, let's just draw the circle first. To understand this concept, we have a trailer homes in battle with 24 rooms. We have a back yard dash in cities with six homes and the batteries off 42 worlds got in. Directions are already given now, since we're using no drool Asper the K jobs current low. So all right, here Asper kill jobs. Current low, occasional desk a CEO, some off the gardens entering the northern is equal to some off the cuttings, living down dead for Senor Hee. And don't be so. The current which is entering into nor a is I six is equal to the currents which are living from nor a R i trow and I 24. So the addition offer it. So finally we got a question as I six is equal to I drove Bless I 24 and will among this has gration one. Now we need to find a question using Lou Prude. So using you're through two battery, which is our 42 wars, six home and 24 homes. So let's draw the circuit again. Which would be the same Sochi, huh? So in this case, we need to consider one particular direction in orderto find individual British jobs across great distances shall again just put the polarities across 24 6 home. Now, by considering this particular diagram we are trying to find okay, just for Did you know I'm in this case? We need to apply key veal to the loo. So it will be a combination of 42 minus six in do I six minus dreadful into I train ful is equal to zero because you just want a law is algebraic sum off all the work ages across resistance is is you. So therefore, finally, we get a question as six high six less 24 i 24 is equal to what you do. Animal. Consider this as immigration, too. Now we need to find the question using Luke rule. So right here using, you know, cruise two duels. I'm sorry. That is 12 rooms and 24 rooms. Yeah, so let's draw the circuit again. The battery's off 42 walls. Try along and training forms again. Acclamation. The polarities asked for the current election and they just move clockwise in order to collect. The world is drop across 12 and dreadful so that is going to be using K chops. Word is law. It is my nurse training for troll less 24 I've 24 is equal to see you because these individual currents are given and we need to good the polarity off. They're leaving term, you know. Day four soldering further. We get 12 I to he's equal to training for I trained for that's dignity Chauffeur that his ID trove I'm going. I 24 is equal to 24 by 12. That is too. So we get the 30 question as I trow is equal to two times I 24. That's ticket as immigration tree Now lettuce substitute this value off. I trow in regression one. All right, Jesse, question one for you So I six is equipped to I trolled Bless. I'm 24 So two times I dreadful unless I'm 24. So therefore the value of current, which is going to six Home is equal to three dimes I train ful. It's marked this equation. No next year Lettuce substitute I six around you. Any question Tube day for six times six. Bless training food times I grateful. Easy, quick Afford you now putting the I six value in this six times multiplied by three times, are 24 bless 24 times I train ful is equal to 42. Therefore, we get it as 42 times. I 24 is equal to 42 and for this all being, we get 24 that it's got inferring through 24. Room is equal to 40 toward upon 40 dorms. That is one up here. This is one of dances for ratification. Next we're trying to substitute again. We're trying to substitute this value off I tray full integration treat dead for I trow is equal to two times I trained for Therefore I troll is equal to two times wanna beer. So far, though we get I troll is equal to two and half years This body of mine which is going through 12 rooms This is a game ready find Next we need to substitute value off I 20 full and they question which is why six is equal to three times I drink ful So three times one I'm beer Richard, you get he does three on beers. Therefore, even the current we're just going to six home. He's all three amperes again. It has been very fine. Sure does. Let's write the conclusion we have verified the current values up gained in Bar Kay off solution.

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